The weight of an organ in adult males has a bell-shaped distribution with a mean
ID: 3042954 • Letter: T
Question
The weight of an organ in adult males has a bell-shaped distribution with a mean of 325 grams and a standard deviation of 20 grams. Use the empirical rule to determine the following.
(A)About 68% of organs will be between what weights?
(B) What percentage of organs weighs between 285 grams and 365 grams? (Type an integer)
(C) What percentage of organs weighs less than 285 grams or more than 365 grams? Type an integer or a decimal.
(D) What percentage of organs weighs between 285 grams and 385 grams? Type an integer or decimal rounded to the nearest hundredth as needed.
Explanation / Answer
a) 68% of organs will be between
= (325-20, 325+20)
= (305 grams , 345 grams)
b) percentage of organs weighs between 285 grams and 365 grams
Since 285 and 365 are 2 standard deviations away from the mean, so by Emipirical rule 95% of data will lies between these values
c) 100-95%
= 5%
d) P(285<X<385)
= P((285-325)/20<Z<(385-325)/20)
= P(-2<Z<3)
= 97.59%
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